I am going to assume that you have already beaten the story and have every campaign card! If not, then go do that now - It shouldn't take more than a day or so, maybe two, if you've just started.
If you HAVE just started and are wondering which starter deck to choose. I would personally pick the Green and White deck.

If you have done that, you should already have all the story achievements, the deck builder achievement, It Must be Mine, and probably the Veteran Explorer achievement.

I am going to go through every achievement, tell you what kind of deck I would run, and where to get it the easiest!
When talking about decks, the most important/best cards for the achievement are in bold, and the cards you don't really need are in italics. Normal text is just what I would use.

NOTE: The best way to get any achievement is probably to make a REALLY bad deck and do a practice duel AGAINST that deck! This is always give you a lot of time and makes it easy to set your stuff up!
The recommended location I list in the guide aren't always better than practice duel, but it's where I would do it if you're not using practice duel - I didn't know about the practice duels before I had all my achievements.

I chose to put these two in the same section, because any deck that will make one of them easy, also makes the other one easy.

Deck
(Green)/White - You don't HAVE to use green, but I feel like it helps a lot!

3x Seraph of the Masses
2x Mentor of the Meek
4x Triplicate Spirits
1x Baneslayer Angel
3x Phantom General
3x Banisher Priest/(Trained Caracal) <-Caracal is only for the achievement, less strong though
1x Brimaz
4x Raise the Alarm
3x Elite Vanguard
If no green:
4x Loyal Pegasus
4x Selfless Cathar

green:
2x Siege Wurm/1x Siege Wurm+1xSoul of Zendikar
2x Scion of the Wild
2x Elder of Laurels
3x Loyal Pegasus/ Chorus of Might
3x Selesnya Evangel

Pick lands as you think will work (I run 4 guildgates, 8 forests, 12 plains)

Just make sure to hit with your Seraph and you will also get Death From Above.

I apologize if there's too many cards there - I tried my best to make it 60. If it's above 60, cut some 1-mana creatures or Siege Wurms.
NOTE: This deck, if you tweak it slightly, is actually competitive on the multiplayer!

Where

I would recommend going to Theros and Explore until you find the treasure chest: What's in the Box?
If you read all of this guide, you will notice that I am going to recommend this place very, very often! The reason is, it actually helps you with almost all the achievements. It has a pretty crappy deck AND puts out creatures for you!

Otherwise, you can pretty much do this anywhere, even in multiplayer. They're really not hard achievements to get. Just stall until it happens.

This one was very tricky for me - With the use of Practice Duel + Bad deck it should be pretty easy, but if you're not using that method, it could take a while to do.

Deck
Blue + Red

4x Vent Sentinel
4x Shock

3x Hedron Crab
2x Kraken Hatchling
4x Cloudfin Raptor
4x Doorkeeper
3x Guard Gomazoa
3x Coral Barrier/3xNullify/3x Wind Drake <- Depends if you have Coral Barriers
4x Inspiration
1x Time Warp

3x Gargoyle Sentinel

4x Guildgate
8x Mountain
13x Island

NOTE: This deck is for the Vent Sentinel achievement - For the Ingenuity achievement, take out the red and put in 4x Tome Scour + 3x Chill of Foreboding + 1x Thassa's Bounty
For the Hedron Crab achievement, put in control spells!

Where

I recommend possibly What's In The Box? in Theros or Show What You Got in Tutorial, but it really isn't easy anyway - I would 100% go Practice Duel with this one!

I really don't understand why this is one of the most rare achievements - It takes a few tries sometimes, but it's not hard to do

Deck
Black

1x Shadowborn Demon
34x Random black cards

Just try to stay alive for a while and then wait for an angel. Then cast Shadowborn Demon and leave/win/lose!

Where

Avacyn in Innistrad is perfect for this, since she tries to get out a bunch of angels - Just wait for one and cast the demon!
You might not win the duel, but you don't need to!

I actually found out that one of the best ways to do this, was to just play my Blue/Red Spell deck!
It may be better to use a deck with a few defenders and guttersnipes, but I'm going to write down my deck, since it's also useful to people who wan to play the multiplayer after the achievements are done!

Deck
Blue Red

3x Voyage's End
3x Guard Gomazoa
3x Dissolve
3x Achaeomancer/2x Talrand + 1x Achaeomancer
1x Inspiration
1x Time Warp
1x Soul of Ravnica

4x Shock
4x Kiln Fiend
4x Krenko's Command
3x Guttersnipe
1x Inferno Titan
1x Siege Dragon

4x Guildgate
11x Island
12x Mountain

Where
If not using the practice duel, you should probably just go into multiplayer until you get it! This deck can actually be a ton of fun to play, though I may need to tweak it a bit.

My favourite achievement name - Raiders of the Lost Arc is truly a classic

Deck
I actually got this achievement just by playing the campaign! Any deck with Nemesis and a lot of creatures should be able to do it, if you go where I'm going to tell you.
If you also want Grateful Dead, you will have to actually win the battle. I recommend using the Green White deck in the Divine Choice section, and putting Nemesis into it instead of some of the less great cards.

Where

Go to Innistrad and fight the Cursed Existence OR even better, go to Shandalar and fight the Wizard's Tower!
He will try to mill you (put things in your graveyard) so you don't need to do much, except draw the Nemesis and some land!

This is another one that I got by just playing the campaign, but let's make an optimal deck for it!
It should be easy enough to get the Second Life achievement with just the Nylea's Disciples - it worked well for me, anyway!

Deck
Mono-Green
Just jam as many green mana symbols as you can in there

2x Elvish Pioneer
2x Genesis Hydra
2x Satyr Wayfinder
2x Scion of the Wild
4x Grave Bramble
1x Vengevine
4x Nylea's Disciple
2x Arbor Colossus
4x Stomper Cub
2x Terra Stomper
2x Phytotitan
3x Nemesis of Mortals
3x Pelekka Wurm
4x Siege Wurm

23x Forest

NOTE: You can also use this deck for the Why Did It Have To Be Snakes? achievement, but it's probably not as viable as some other options.

Where

Either What's In The Box? in Theros Explore or, if you are going for the Why Did It Have To Be Snakes? achievement, go to Wizard's tower in Shandalar Explore

Now, for me, this achievement was really weird, I got it by playing the campaign, and the opponent cast the last aura on my guy.. And it was a GOOD aura for me, too?!
But without the luck of the irish, the best idea would be a Heroic deck.

Deck
White Black

3x Elite Vanguard
4x Loyal Pegasus
2x Hero of Iroas
4x Nimbus Wings
1x Brimaz
3x Banisher Priest
3x Armored Ascension
2x Marked by Honor
1x Baneslayer Angel

3x Tormented Hero
2x Dead Weight
4x Deviant Glee
2x Bloodghast
2x Agent of the Fates

12x Plains
8x Swamp
4x Guildgate

Where

Anywhere should be okay, but just in case you're just as lucky as I am, the Theros explore node Polis Invasion might actually give you auras to help you. All in all, this achievement isn't that hard to get!

I don't really know why this achievement has that name, because it has nothing to do with creatures. As far as I can see, the only way to get it is with Counterlash.
EDIT: Kane pointed out that you can also do this achievement by casting a Convoke spell by tapping only creatures! This option may be a LOT easier than pulling off a counterlash - If you want to use this method, refer to the first achievement in this guide for a Green White Convoke deck. If you have Premium cards, you can use the 1 mana green spell that gives +2/+2 with Convoke! You can potentially pull this achievement off on turn 2.

Deck
You can either put counterlash into the Guttersnipe deck, or:

Mono-blue

4x Cloudfin Raptor
3x Quickling <-Seriously, this guy is underrated
4x Voyage's End
2x Chasm Skulker <- Who is slightly overrated
3x Guard Gomazoa
3x Dissolve
2x Bident of Thassa
4x Achaeomancer
4x Inspiration
1x Time Warp
1x Soul of Ravnica
2x Roil Elemental
2x Counterlash

25x Island

This might not be the BEST deck, but it will work and probably won't take very long.
All you need to do is cast Counterlash on something.

Where

Anywhere! Multiplayer will work, but it's probably easier to go against the Tutorial boss!

This is a fun one! If you're a nice person, do it in multiplayer, to give your opponent a free win.

Deck
Mono-blue

2x Quicken
3x Hedron Crab
4x Kraken Hatchling
4x Cloudfin Raptor
4x Triton Shorestalker
3x Fleeting Distraction
4x Tome Scour
4x Void Snare
4x Artful Dodge
4x Voyage's End/4x Traveler's Amulet

24x Island

Just wait until you have 5 lands out, and cast your spells. Simple!

Where

Either multiplayer or literally any campaign that isn't an aggro deck. The easiest is Zendikar's Trap Lair in Explore.

This was a fun one to get!
My first thought was that I should get a bunch of flashback spells and hope to use them a lot. But there is a MUCH easier way.

Deck
Mono-Blue

2x Quicken (just to draw cards/thin the deck)
3x Hedron Crab
4x Kraken Hatchling
4x Cloudfin Raptor
4x Triton Shorestalker
4x Fleeting Distraction (Same as Quicken)
4x Void Snare
4x Voyage's End
3x Quickling
1x Anything. You should be fine.

27x Island

Just play a creature and put it back in your hand until it's happened 5 times - this worked on my first try!

Where

Just like the Spellstorm achievement, if you're nice, go into multiplayer - else go to the Trap Lair in Zendikar Explore

When I saw this achievement, I actually laughed because I thought the concept was so amusing.

Deck
Black Red

3x Ulcerate
4x Dead Weight
2x Bloodghast
4x Child of Night
2x Walking Corpse
4x Bloodflow Connoisseur
4x Corpse Blockade
4x Devouring Swarm
4x Act of Treason
4x Portent of Betrayal

4x guildgate
14x Swamp
6x Mountain

Just use either of the red spells and then one of the three sacrifice creatures to get the job done!

Where

I did this on Avacyn because I mixed this and the Shadowborn Demon achievement, but you can do it on anyone, anywhere. Preferably against a deck with a lot of creatures of course

The last one I got. At 4 AM.. I was so tired.
Thankfully it worked on the 2nd try for me, though it is VERY much about luck.
Also, fun fact. You can't have more than 50% land in this game, and you can't have more than 50 of a single land - I learned that while trying to find the perfect deck for this (I was going to just use the elf and cultivate, then 52 land)

Deck
Mono-Green

4x Elvish Pioneer
3x Primal Bellow
4x Fog
2x Genesis Hydra
4x Elvish Visionary
1x Timberland Guide
4x Satyr Wayfinder
4x Grazing Gladeheart
4x Cultivate

30x Forest

Apart from the four bolded spells, you can really choose whatever you want

Where

Anywhere you think you can make it to turn 4! (So.. Anywhere)

So, I don't actually have this one yet, because it takes a VERY long time to even play 100 games, let alone win them, but I will just post the deck I am using for it.
I have chosen this deck, not because it's the strongest, but because it's the FASTEST.
It wins almost as much, if not as much, as the best decks, but the bonus is that if it wins, it wins on turn 4-5 most of the time.

Deck
Mono-Red Goblins

3x Quest for the Goblin Lord
3x Coordinated Assault
4x Goblin Arsonist
4x Foundry Street Denizen
4x Shock
4x Krenko's Command
2x Goblin Rabblemaster
3x Guttersnipe/Goblin Bushwhacker
4x Trumpet Blast
2x Ogre Battledriver
4x Demolish/3x Paragon of Fierce Defiance + 1x Demolish

22x Mountain

I think it might need some tweaking to be optimal, but this is what I've got so far, and it does pretty darn well!

Thanks for reading the guide! I hope it helped you in some way.

If you have any questions, suggestions or.. well anything at all, you can either comment down below, or just add me on steam! I'll gladly accept.

If you need help with any of the achievements, I'll gladly help by joining a multiplayer game with you and use a deck that can help you (Like a bounce-deck for Rampant Growth)

Cheers!

-Zypre